Abstract

In certain cases, images of different scenes can be mixed to produce an image of a novel scene. For example, an image of a pink sphere can be additively mixed from suitable images of a red and a white sphere. Three ways in which scenes can differ are considered: in the spectral composition of the illuminant and in the spectral and the geometric reflectance of scene objects. Sufficient conditions are given for mixing to produce images that correspond to possible scenes. Examples illustrate ways that mixtures can be used as stimuli in psychophysical experiments concerned with pictorial perception.

© 1999 Optical Society of America

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References

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  1. N. J. Wade, A Natural History of Vision (MIT Press, Cambridge, Mass., 1998).
  2. J. D. Forbes, “Hints towards a classification of colours,” Philos. Mag. 34 (1948).
  3. J. C. Maxwell, “Theory of the perception of colours,” Trans. R. Scott. Soc. Arts 4, 394–400 (1856).
  4. J. C. Maxwell, “The diagram of colours,” Trans. R. Soc. Edinburgh 21, 275–298 (1857).
    [CrossRef]
  5. L. D. Griffin, “Production of psychophysical stimuli by partitive mixing of images,” Perception 27(suppl.), 171–172 (1998).
  6. J. C. Maxwell, “Theory of compound colours, and the relations of the colours on the spectrum,” Proc. R. Soc. London 10, 404–409 (1860).
    [CrossRef]
  7. J. J. Koenderink, “Color atlas theory,” J. Opt. Soc. Am. A 4, 1314–1321 (1987).
    [CrossRef]
  8. P. Turner, “Building a colour image mixing system,” B. Optom. dissertation (Aston University, Birmingham, England, 1998).
  9. S. Lee, G. Wolberg, S. Y. Shin, “Polymorph: morphing among multiple images,” IEEE Comput. Graph. Appl. 18, 58–71 (1988).
  10. Informally, an affine space is a vector space lacking a point singled out as the origin; a familiar example is the space of equally luminous colors depicted in the CIE diagram. Formally, it is a space of points with an associated vector space and two permissible operations: (i) One may form the difference of two points, which is a vector in the associated vector space, and (ii) one may add any vector to any point to form a new point. However, unlike for a vector space, one cannot multiply a point by a scalar nor add together two points.
  11. P. E. Debevec, J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proceedings of the Special Interest Group on Graphics ’97 (Proc. SIGGRAPH ’97) (Addison-Wesley, Reading, Mass., 1997), pp. 369–378.
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
  19. C. M. Goral, K. E. Torrance, D. P. Greenberg, B. Battaile, “Modelling the interaction of light between diffuse surfaces,” Comput. Graph. 18, 212–222 (1984).
    [CrossRef]
  20. B. V. Funt, M. S. Drew, J. Hio, “Color constancy from mutual reflection,” Int. J. Comput. Vision 6, 5–24 (1991).
    [CrossRef]
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  22. J. J. Koenderink, A. J. van Doorn, “Phenomenological description of bidirectional surface reflection,” J. Opt. Soc. Am. A 15, 2903–2912 (1998).
    [CrossRef]
  23. If the basis images were out of focus (and so blurred), for example, then an sp mixture that had zero-valued pixels could not correspond to any object.
  24. A. J. van Doorn, “Effects of changing context on shape perception,” Perception 27, S117 (1998).
  25. D. H. Brainard, M. D. Rutherford, J. M. Kraft, “Colour constancy compared: experiments with real images and color monitors,” Invest. Ophthalmol. Visual Sci. 38, S2206 (1997).
  26. A. Hurlbert, “Illusions and reality checking on the small screen,” Perception 27, 633–636 (1998).
  27. R. L. Savoy, “Colour constancy with reflected and emitted light,” Perception 22S, 61 (1993).
  28. The psychological distinctness of “it looks X” and “it can be seen as X” was noted by Wittgenstein (Ref. 29). An example of the difference is in regard to the three-dimensionality of line drawings. Suppose that one is examining a straightforward sketch of a cube (which one recognizes as such), and is asked “Does it look three-dimensional?” One could reasonably answer either yes or no. In contrast, “Can you see it as three-dimensional?” could reasonably only be answered yes. “Reasonably” here should be understood as “speaking the same language.”
  29. L. Wittgenstein, Philosophical Investigations (Blackwells, Oxford, U.K., 1953).
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

1998 (4)

L. D. Griffin, “Production of psychophysical stimuli by partitive mixing of images,” Perception 27(suppl.), 171–172 (1998).

J. J. Koenderink, A. J. van Doorn, “Phenomenological description of bidirectional surface reflection,” J. Opt. Soc. Am. A 15, 2903–2912 (1998).
[CrossRef]

A. J. van Doorn, “Effects of changing context on shape perception,” Perception 27, S117 (1998).

A. Hurlbert, “Illusions and reality checking on the small screen,” Perception 27, 633–636 (1998).

1997 (2)

D. H. Brainard, M. D. Rutherford, J. M. Kraft, “Colour constancy compared: experiments with real images and color monitors,” Invest. Ophthalmol. Visual Sci. 38, S2206 (1997).

A. J. den Dekker, A. ven den Bos, “Resolution: a survey,” J. Opt. Soc. Am. A 14, 547–557 (1997).
[CrossRef]

1996 (1)

1993 (2)

R. L. Savoy, “Colour constancy with reflected and emitted light,” Perception 22S, 61 (1993).

J. J. Gordon, R. A. Holub, “On the use of linear transformations for scanner calibration,” Color Res. Appl. 18, 218–219 (1993).
[CrossRef]

1991 (2)

B. V. Funt, M. S. Drew, J. Hio, “Color constancy from mutual reflection,” Int. J. Comput. Vision 6, 5–24 (1991).
[CrossRef]

M. D. Fairchild, E. Pirrotta, “Predicting the lightness of chromatic object colours using CIELAB,” Col. Res. Appl. 16, 385–393 (1991).
[CrossRef]

1988 (1)

S. Lee, G. Wolberg, S. Y. Shin, “Polymorph: morphing among multiple images,” IEEE Comput. Graph. Appl. 18, 58–71 (1988).

1987 (1)

1986 (1)

B. A. Wandell, “Color rendering of color camera data,” Color Res. Appl. 11, S30–S33 (1986).

1984 (1)

C. M. Goral, K. E. Torrance, D. P. Greenberg, B. Battaile, “Modelling the interaction of light between diffuse surfaces,” Comput. Graph. 18, 212–222 (1984).
[CrossRef]

1983 (1)

J. J. Koenderink, A. J. van Doorn, “Geometrical modes as a method to treat diffuse inter-reflections in radiometry,” J. Opt. Soc. Am. A 73, 843–850 (1983).
[CrossRef]

1982 (1)

1967 (1)

1961 (1)

1959 (1)

1948 (1)

J. D. Forbes, “Hints towards a classification of colours,” Philos. Mag. 34 (1948).

1926 (1)

1920 (1)

E. Schrödinger, “Theorie der Pigmente von grosster Leuchtkraft,” Ann. Phys. 62, 603–622 (1920).
[CrossRef]

1860 (1)

J. C. Maxwell, “Theory of compound colours, and the relations of the colours on the spectrum,” Proc. R. Soc. London 10, 404–409 (1860).
[CrossRef]

1857 (1)

J. C. Maxwell, “The diagram of colours,” Trans. R. Soc. Edinburgh 21, 275–298 (1857).
[CrossRef]

1856 (1)

J. C. Maxwell, “Theory of the perception of colours,” Trans. R. Scott. Soc. Arts 4, 394–400 (1856).

Battaile, B.

C. M. Goral, K. E. Torrance, D. P. Greenberg, B. Battaile, “Modelling the interaction of light between diffuse surfaces,” Comput. Graph. 18, 212–222 (1984).
[CrossRef]

Brainard, D. H.

D. H. Brainard, M. D. Rutherford, J. M. Kraft, “Colour constancy compared: experiments with real images and color monitors,” Invest. Ophthalmol. Visual Sci. 38, S2206 (1997).

J. M. Spiegle, D. H. Brainard, “Luminosity thresholds: effect of test chromaticity and ambient illumination,” J. Opt. Soc. Am. A 13, 436–451 (1996).
[CrossRef]

Debevec, P. E.

P. E. Debevec, J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proceedings of the Special Interest Group on Graphics ’97 (Proc. SIGGRAPH ’97) (Addison-Wesley, Reading, Mass., 1997), pp. 369–378.

den Dekker, A. J.

Drew, M. S.

B. V. Funt, M. S. Drew, J. Hio, “Color constancy from mutual reflection,” Int. J. Comput. Vision 6, 5–24 (1991).
[CrossRef]

Evans, R. M.

Fairchild, M. D.

M. D. Fairchild, E. Pirrotta, “Predicting the lightness of chromatic object colours using CIELAB,” Col. Res. Appl. 16, 385–393 (1991).
[CrossRef]

Forbes, J. D.

J. D. Forbes, “Hints towards a classification of colours,” Philos. Mag. 34 (1948).

Funt, B. V.

B. V. Funt, M. S. Drew, J. Hio, “Color constancy from mutual reflection,” Int. J. Comput. Vision 6, 5–24 (1991).
[CrossRef]

Ginsberg, I. W.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (National Bureau of Standards, Washington, D.C., 1977).

Goral, C. M.

C. M. Goral, K. E. Torrance, D. P. Greenberg, B. Battaile, “Modelling the interaction of light between diffuse surfaces,” Comput. Graph. 18, 212–222 (1984).
[CrossRef]

Gordon, J. J.

J. J. Gordon, R. A. Holub, “On the use of linear transformations for scanner calibration,” Color Res. Appl. 18, 218–219 (1993).
[CrossRef]

Greenberg, D. P.

C. M. Goral, K. E. Torrance, D. P. Greenberg, B. Battaile, “Modelling the interaction of light between diffuse surfaces,” Comput. Graph. 18, 212–222 (1984).
[CrossRef]

Griffin, L. D.

L. D. Griffin, “Production of psychophysical stimuli by partitive mixing of images,” Perception 27(suppl.), 171–172 (1998).

Hio, J.

B. V. Funt, M. S. Drew, J. Hio, “Color constancy from mutual reflection,” Int. J. Comput. Vision 6, 5–24 (1991).
[CrossRef]

Holub, R. A.

J. J. Gordon, R. A. Holub, “On the use of linear transformations for scanner calibration,” Color Res. Appl. 18, 218–219 (1993).
[CrossRef]

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (National Bureau of Standards, Washington, D.C., 1977).

Hurlbert, A.

A. Hurlbert, “Illusions and reality checking on the small screen,” Perception 27, 633–636 (1998).

Koenderink, J. J.

Kraft, J. M.

D. H. Brainard, M. D. Rutherford, J. M. Kraft, “Colour constancy compared: experiments with real images and color monitors,” Invest. Ophthalmol. Visual Sci. 38, S2206 (1997).

Lee, S.

S. Lee, G. Wolberg, S. Y. Shin, “Polymorph: morphing among multiple images,” IEEE Comput. Graph. Appl. 18, 58–71 (1988).

Limperis, T.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (National Bureau of Standards, Washington, D.C., 1977).

Malik, J.

P. E. Debevec, J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proceedings of the Special Interest Group on Graphics ’97 (Proc. SIGGRAPH ’97) (Addison-Wesley, Reading, Mass., 1997), pp. 369–378.

Maxwell, J. C.

J. C. Maxwell, “Theory of compound colours, and the relations of the colours on the spectrum,” Proc. R. Soc. London 10, 404–409 (1860).
[CrossRef]

J. C. Maxwell, “The diagram of colours,” Trans. R. Soc. Edinburgh 21, 275–298 (1857).
[CrossRef]

J. C. Maxwell, “Theory of the perception of colours,” Trans. R. Scott. Soc. Arts 4, 394–400 (1856).

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (National Bureau of Standards, Washington, D.C., 1977).

Pirrotta, E.

M. D. Fairchild, E. Pirrotta, “Predicting the lightness of chromatic object colours using CIELAB,” Col. Res. Appl. 16, 385–393 (1991).
[CrossRef]

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (National Bureau of Standards, Washington, D.C., 1977).

Ronchi, V.

Rutherford, M. D.

D. H. Brainard, M. D. Rutherford, J. M. Kraft, “Colour constancy compared: experiments with real images and color monitors,” Invest. Ophthalmol. Visual Sci. 38, S2206 (1997).

Savoy, R. L.

R. L. Savoy, “Colour constancy with reflected and emitted light,” Perception 22S, 61 (1993).

Schrödinger, E.

E. Schrödinger, “Theorie der Pigmente von grosster Leuchtkraft,” Ann. Phys. 62, 603–622 (1920).
[CrossRef]

Shafer, S. A.

Shin, S. Y.

S. Lee, G. Wolberg, S. Y. Shin, “Polymorph: morphing among multiple images,” IEEE Comput. Graph. Appl. 18, 58–71 (1988).

Spiegle, J. M.

Torrance, K. E.

C. M. Goral, K. E. Torrance, D. P. Greenberg, B. Battaile, “Modelling the interaction of light between diffuse surfaces,” Comput. Graph. 18, 212–222 (1984).
[CrossRef]

Turner, P.

P. Turner, “Building a colour image mixing system,” B. Optom. dissertation (Aston University, Birmingham, England, 1998).

van Doorn, A. J.

A. J. van Doorn, “Effects of changing context on shape perception,” Perception 27, S117 (1998).

J. J. Koenderink, A. J. van Doorn, “Phenomenological description of bidirectional surface reflection,” J. Opt. Soc. Am. A 15, 2903–2912 (1998).
[CrossRef]

J. J. Koenderink, A. J. van Doorn, “Geometrical modes as a method to treat diffuse inter-reflections in radiometry,” J. Opt. Soc. Am. A 73, 843–850 (1983).
[CrossRef]

ven den Bos, A.

Wade, N. J.

N. J. Wade, A Natural History of Vision (MIT Press, Cambridge, Mass., 1998).

Wandell, B. A.

B. A. Wandell, “Color rendering of color camera data,” Color Res. Appl. 11, S30–S33 (1986).

Wittgenstein, L.

L. Wittgenstein, Philosophical Investigations (Blackwells, Oxford, U.K., 1953).

Wolberg, G.

S. Lee, G. Wolberg, S. Y. Shin, “Polymorph: morphing among multiple images,” IEEE Comput. Graph. Appl. 18, 58–71 (1988).

Wyszecki, G.

Yaumauti, Z.

Ann. Phys. (1)

E. Schrödinger, “Theorie der Pigmente von grosster Leuchtkraft,” Ann. Phys. 62, 603–622 (1920).
[CrossRef]

Col. Res. Appl. (1)

M. D. Fairchild, E. Pirrotta, “Predicting the lightness of chromatic object colours using CIELAB,” Col. Res. Appl. 16, 385–393 (1991).
[CrossRef]

Color Res. Appl. (2)

J. J. Gordon, R. A. Holub, “On the use of linear transformations for scanner calibration,” Color Res. Appl. 18, 218–219 (1993).
[CrossRef]

B. A. Wandell, “Color rendering of color camera data,” Color Res. Appl. 11, S30–S33 (1986).

Comput. Graph. (1)

C. M. Goral, K. E. Torrance, D. P. Greenberg, B. Battaile, “Modelling the interaction of light between diffuse surfaces,” Comput. Graph. 18, 212–222 (1984).
[CrossRef]

IEEE Comput. Graph. Appl. (1)

S. Lee, G. Wolberg, S. Y. Shin, “Polymorph: morphing among multiple images,” IEEE Comput. Graph. Appl. 18, 58–71 (1988).

Int. J. Comput. Vision (1)

B. V. Funt, M. S. Drew, J. Hio, “Color constancy from mutual reflection,” Int. J. Comput. Vision 6, 5–24 (1991).
[CrossRef]

Invest. Ophthalmol. Visual Sci. (1)

D. H. Brainard, M. D. Rutherford, J. M. Kraft, “Colour constancy compared: experiments with real images and color monitors,” Invest. Ophthalmol. Visual Sci. 38, S2206 (1997).

J. Opt. Soc. Am. (5)

J. Opt. Soc. Am. A (5)

Perception (4)

A. Hurlbert, “Illusions and reality checking on the small screen,” Perception 27, 633–636 (1998).

R. L. Savoy, “Colour constancy with reflected and emitted light,” Perception 22S, 61 (1993).

A. J. van Doorn, “Effects of changing context on shape perception,” Perception 27, S117 (1998).

L. D. Griffin, “Production of psychophysical stimuli by partitive mixing of images,” Perception 27(suppl.), 171–172 (1998).

Philos. Mag. (1)

J. D. Forbes, “Hints towards a classification of colours,” Philos. Mag. 34 (1948).

Proc. R. Soc. London (1)

J. C. Maxwell, “Theory of compound colours, and the relations of the colours on the spectrum,” Proc. R. Soc. London 10, 404–409 (1860).
[CrossRef]

Trans. R. Scott. Soc. Arts (1)

J. C. Maxwell, “Theory of the perception of colours,” Trans. R. Scott. Soc. Arts 4, 394–400 (1856).

Trans. R. Soc. Edinburgh (1)

J. C. Maxwell, “The diagram of colours,” Trans. R. Soc. Edinburgh 21, 275–298 (1857).
[CrossRef]

Other (8)

P. Turner, “Building a colour image mixing system,” B. Optom. dissertation (Aston University, Birmingham, England, 1998).

Informally, an affine space is a vector space lacking a point singled out as the origin; a familiar example is the space of equally luminous colors depicted in the CIE diagram. Formally, it is a space of points with an associated vector space and two permissible operations: (i) One may form the difference of two points, which is a vector in the associated vector space, and (ii) one may add any vector to any point to form a new point. However, unlike for a vector space, one cannot multiply a point by a scalar nor add together two points.

P. E. Debevec, J. Malik, “Recovering high dynamic range radiance maps from photographs,” in Proceedings of the Special Interest Group on Graphics ’97 (Proc. SIGGRAPH ’97) (Addison-Wesley, Reading, Mass., 1997), pp. 369–378.

N. J. Wade, A Natural History of Vision (MIT Press, Cambridge, Mass., 1998).

The psychological distinctness of “it looks X” and “it can be seen as X” was noted by Wittgenstein (Ref. 29). An example of the difference is in regard to the three-dimensionality of line drawings. Suppose that one is examining a straightforward sketch of a cube (which one recognizes as such), and is asked “Does it look three-dimensional?” One could reasonably answer either yes or no. In contrast, “Can you see it as three-dimensional?” could reasonably only be answered yes. “Reasonably” here should be understood as “speaking the same language.”

L. Wittgenstein, Philosophical Investigations (Blackwells, Oxford, U.K., 1953).

If the basis images were out of focus (and so blurred), for example, then an sp mixture that had zero-valued pixels could not correspond to any object.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsberg, T. Limperis, “Geometrical considerations and nomenclature for reflectance,” NBS Monograph 160 (National Bureau of Standards, Washington, D.C., 1977).

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Figures (8)

Fig. 1
Fig. 1

Top, Euclidean embedding of the mixture space of three basis images. One can determine the weighting of the basis images needed to produce the mixture image at any given point by considering what masses (with unit sum) placed at the locations of the basis images would have a center of gravity at the point. Bottom left, noise variance level for different mixtures; bottom right, maximum magnitude of misregistration artifacts for different mixtures.

Fig. 2
Fig. 2

Results of an evaluation of the accuracy with which mixed images simulate real images. Bottom half, blurred visions of the basis images D and L were used to generate mixtures that matched the blurred targets B, G, and W. At the top left are details showing regions of a target and a mixture image that can easily be seen to be different if mixing is done with unblurred images (frames in the lower part of the figure show the locations of these regions of interest). The graph shows how the mismatch between mixed and target images decreases with blurring.

Fig. 3
Fig. 3

Results of mixing images acquired through filters of different colors (equivalent to using differently colored illuminants). Top row: basis images. Bottom row: (a) is a p mixture 〈0.28, 0.25, 0.47〉; and (b) and (c) are sp, 〈-0.11, 0.59, 0.52〉 and 〈0.33, -0.54, 1.21〉, respectively.  

Fig. 4
Fig. 4

Results of mixing images of objects of different colors. Top row: basis images. Bottom row: left, a genuine image; right, the sp mixture 〈0.97, 0.65, 0.25, -0.87〉 that most closely approximates it.

Fig. 5
Fig. 5

Left, a genuine image; right, an sp mixture with the same weights as in Fig. 4. Note the differences between the two images on the left side of the sphere and on the white cup next to it. These differences are due to the failure of the technique in scenes with significant interreflection involving the changing object.

Fig. 6
Fig. 6

Results of mixing images of objects with different geometric reflectance properties. Top row: basis images. Bottom row: (a) is a p mixture 〈0.52, 0.37, 0.11〉; (b) and (c) are sp, 〈0, -1, 2〉 and 〈-0.5, 1, 0.5〉, respectively.  

Fig. 7
Fig. 7

Results of an experiment mapping the limit of realism that occurs in the space of mixtures of a black, a cream-white, and a red sphere. The small density maps (top left) show, for three subjects, the proportion of trials in which different mixtures were judged possible to see as realistic, from white (100%) to black (0%). The larger map is the average across subjects. The red contour shows the 50% threshold. Individual mixtures, displayed with the D function used in the experiment, correspond to the locations marked a–l.

Fig. 8
Fig. 8

Results of an experiment on lightness perception. Subjects judged whether a mixture u1, u2 of a cream-white and a black sphere was lighter or darker than a mixture w1, w2, w3 of a red, a green, and a blue sphere. The stimuli u1, u2|w1, w2, w3 on which the judgments were based were created from the four basis images on the top row by the mixture 1-u1-w2,u1-w3, w2, w3. Lightness matches were determined by fitting psychometric functions to the judgment data. These matches are shown (bottom left) as contours of equal cream-white ball content. An empirically determined lightness match 0.2, 0.8|1/3, 1/3, 1/3 is shown at the bottom right.  

Equations (4)

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m(w1,, wn)=maxs{1,,n}miniswi, 1-iswi.
P(L)=4.44L,L0.02981.27(L0.324-0.217),otherwise,
rigibi[d¯r(lr,i-ri)+l¯r(ri-dr,i)]/(lr,i-dr,i)[d¯g(lg,i-gi)+l¯g(gi-dg,i)]/(lg,i-dg,i)[d¯b(lb,i-bi)+l¯b(bi-db,i)]/(lb,i-db,i)
u1, u2matchesinlightnessw1, w2, w3

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